Related papers: Optimal stopping, randomized stopping and singular…
A general result on the method of randomized stopping is proved. It is applied to optimal stopping of controlled diffusion processes with unbounded coefficients to reduce it to an optimal control problem without stopping. This is motivated…
This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…
In this study, we adopt age of information as a measure of the staleness of information, and take initial steps towards analyzing the control performance of stochastic systems with stale information. Our goals are to cast light on a…
This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
Many decision problems in economics, information technology, and industry can be transformed to an optimal stopping of adapted random vectors with some utility function over the set of Markov times with respect to filtration build by the…
Many discrete-time optimal stopping problems are known to have more tractable limit forms based on a planar Poisson process. Using this tool we find a solution to the optimal stopping problem for i.i.d. sequence of $n$ discrete uniform…
In a classical optimal stopping problem the aim is to maximize the expected value of a functional of a diffusion evaluated at a stopping time. This note considers optimal stopping problems beyond this paradigm. We study problems in which…
In this paper, we study a class of stochastic optimal control problem with jumps under partial information. More precisely, the controlled systems are described by a fully coupled nonlinear multi- dimensional forward-backward stochastic…
We formulate a very general framework for optimal dynamic stochastic control problems which allows for a control-dependent informational structure. The issue of informational consistency is investigated. Bellman's principle is formulated…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
We extend the classical setting of an optimal stopping problem under full information to include for problems with an unknown state. The framework allows the unknown state to influence (i) the drift of the underlying process, (ii) the…
We develop methods to solve general optimal stopping problems with opportunities to stop that arrive randomly. Such problems occur naturally in applications with market frictions. Pivotal to our approach is that our methods operate on…
In this paper the connection between stochastic optimal control and reinforcement learning is investigated. Our main motivation is to apply importance sampling to sampling rare events which can be reformulated as an optimal control problem.…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
In this study, we consider an optimal control problem driven by a stochastic differential system with a stopping time terminal cost functional. We establish the stochastic maximum principle for this new kind of an optimal control problem by…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
In this paper we consider a control problem for a Partially Observable Piecewise Deterministic Markov Process of the following type: After the jump of the process the controller receives a noisy signal about the state and the aim is to…